PHYSICAL REVIEW A 98, 052707 (2018) Rovibrational excitation of rare-gas dimers by electron impact E. P. Seidel * and F. Arretche † Departamento de Física, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, Santa Catarina, Brazil (Received 15 March 2018; revised manuscript received 6 September 2018; published 27 November 2018) Electron scattering by rare-gas dimers is studied for very low incident energies using the zero range potential (ZRP) method. Beyond the traditional ZRP, we consider an alternative formulation accounting for the atomic polarization, inspired in the modified effective range theory. The scattering calculations are reported in fixed nuclei, rigid rotor, and rovibrational approximations, the first two being analytical. An expression for the electron-molecule scattering length is obtained. We find that short-range interactions are the dominant mechanism for rotational transitions in electron scattering by rare-gas dimers, while the long-range interactions may be neglected. Our results show how the elastic, rotational, and rovibrational cross sections depend on the electron-atom scattering length, on the molecular parameters, and also on the inclusion of polarization effects. The principle of detailed balance is discussed in the context of the ZRP method. Finally, we show that the rovibrational coupling considerably affects the rotational cross sections when the rotational constant becomes comparable to the vibrational constant. DOI: 10.1103/PhysRevA.98.052707 I. INTRODUCTION When an environment composed by noble gas atoms finds proper thermodynamic conditions, there exists a probability that these atoms interact between themselves through van der Waals forces, forming dimers [1,2]. The rare-gas dimers have been the subject of a broad spectroscopic investigation performed by Tanaka and Yoshino for He 2 , Ne 2 , and Ar 2 [3–5], by Tanaka et al. for Kr 2 [6], and by Freeman et al. for Xe 2 [7]. Since then, such dimers have been extensively studied in order to establish potentials that properly describe the molecular properties (see, for example, Slavíˇ cek et al. [8] and Tang and Toennies [9]). Such a task has shown to be a difficult one. For He 2 , for instance, Cybulski and Toczylowski reported an ab initio potential that is not even deep enough to support a vibrational bound state [10], while it does exist for the potential calculated by Janzen and Aziz [11]. As far as we could verify, very few explicit studies about electron scattering by neutral van der Waals dimers have been reported in literature so far. Sweeping the 8.0–8.9 energy- loss range and paying attention to the Feshbach resonances associated to the Xe 3 P 2 and 3 P 1 atomic lines, Allan measured the electron impact spectra of Xe 2 and Xe n (n ∼ 3, 4) [12] and observed that such structures are practically absent in the dimers. More recently, Blanco and Garcia [13] computed electron-Ar 2 scattering cross sections between 1 and 500 eV using the screening corrected additivity rule combined with the independent atom representation. This technique is able to generate elastic, inelastic, and total cross sections but does not take into account the rotational and vibrational dynamics of the target. On the other side, through the years, more attention has been given to the problem of electron scattering by * e.p.seidel@posgrad.ufsc.br † f.arretche@ufsc.br rare-gas ionized dimers, the so-called dissociative recombi- nation: e − + R 2 + → R + R + kinetic energy [14–18]. Investigations on e − + X 2 (X = He, Ne, Ar, Kr, and Xe) dimers are, in fact, scarce. In principle, the associated cross sections could be calculated with well-established methods like the R matrix [19] or the complex Kohn [20]. The com- putation of electron-molecule cross sections is specially hard for very low incident electron energies, mainly about what concerns the incorporation of the target-projectile correlation- polarization effects and the proper evaluation of the vibra- tional and rotational couplings. Considering the very-low-energy regime, we find a suitable method known as the zero range potential (ZRP) [21]. In this approach the effect of the scattering potential is reduced to a boundary condition. The greatest advantage of using the ZRP is that the calculation is strongly simplified when compared to more sophisticated treatments, and analytical solutions may be found for some particular cases. It works as a semiempiri- cal method because the working expressions for the cross sec- tions depend on parameters like the electron-atom scattering length or the atomic dipole polarizability in such a way that it is possible to investigate how the cross sections vary with different values for each atomic and molecular parameter. ZRP is a successful methodology that has been applied to the electron-molecule scattering problem. Drukarev and Yurova used it combined with the adiabatic approximation to calculate rotational and vibrational cross sections for electron- H 2 , Li 2 , Na 2 , and K 2 impact [22]. In a similar way, Ostrovsky and Ustimov obtained the exact solution of the particle-rigid- rotor scattering problem [23], based on the ZRP formulation. Later, Gribakin demonstrated, using the ZRP, that positron annihilation with molecules can be enhanced due to Feshbach vibrational resonances [24]. Finally, Leble and Yalunin ap- plied the ZRP to calculate the X 1  g + → a 3  g + electronic and vibrational excitation cross sections of H 2 by electron impact [25,26]. 2469-9926/2018/98(5)/052707(15) 052707-1 ©2018 American Physical Society